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Lesson 2: Forward Contracts I Part 1

The Net Present Value of Forward Contract

The forward price is such that NPV of an at-market Forward contract = 0

  • Because an at-market forward has no arbitrage profit making opportunity
  • Because the exercise price of a contract = PV(the spot price at t = 0, net of income from the underlying, plus carrying cost of the underlying)
Example 2.4. (of NPV Calculation of a Forward Contract):

The IBM stock is currently traded at $180. A stock dealer offers a 6-month forward (or futures) on IBM at $185.32.

Assume the risk-free rate, r0, is 6% and there will be no dividend payment within six months. How would you calculate the NPV of a long forward contract?

Click on Example 2.4. Solution to view the solution.

Example 2.4. Solution:

Under the long forward, the buyer will pay $185.32 and receive one share of IBM stock in 6 months. Therefore,
(NPV of the forward) = -PV($185.32) + PV (1 share of IBM stock in 6 months).

  1. PV($185.32) = $185.32/(1 + 6%)∧0.5 = 180
  2. One share of IBM stock in 6 month is financially equivalent to one share of IBM stock now because there is no dividend payment, which is worth $180 today, i.e., the PV(IBM share at maturity) = $180.

Therefore NPV = - 180 + 180 = 0

NPV of Forward Contracts: The forward price is such that NPV of an equilibrium-priced forward contract = 0

  • Because an equilibrium-priced forward has no arbitrage profit making opportunity
the forward price of a contract
= (the spot price at t = 0)
- FV(net of income from the underlying)
+ FV(carrying cost of the underlying)

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